Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2003-10-02
Phys.Rev. D70 (2004) 096013
Physics
High Energy Physics
High Energy Physics - Phenomenology
19 pages, 4 figures; minor clarifications, additional figure
Scientific paper
10.1103/PhysRevD.70.096013
Two new sum rules were recently discovered by Le Yaouanc et al. by applying the operator product expansion to the nonforward matrix element of a time-ordered product of $b \to c$ currents in the heavy-quark limit of QCD. They lead to the constraints $\sigma^2 > 5\rho^2/4$ and $\sigma^2 > 3(\rho^2)^2/5 + 4\rho^2/5$ on the curvature of the $\bar{B} \to D^{(*)}$ Isgur-Wise function, both of which imply the absolute lower bound $\sigma^2 > 15/16$ when combined with the Uraltsev bound $\rho^2 > 3/4$ on the slope. This paper calculates order $\alpha_s$ corrections to these bounds, increasing the accuracy of the resultant constraints on the physical form factors. The latter may have implications for the determination of $|V_{cb}|$ from exclusive semileptonic $B$ meson decays.
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